This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A054880 #64 Aug 22 2025 17:40:31
%S A054880 0,6,60,546,4920,44286,398580,3587226,32285040,290565366,2615088300,
%T A054880 23535794706,211822152360,1906399371246,17157594341220,
%U A054880 154418349070986,1389765141638880,12507886274749926,112570976472749340,1013138788254744066,9118249094292696600,82064241848634269406,738578176637708424660
%N A054880 a(n) = 3*(9^n - 1)/4.
%C A054880 Number of walks of length 2n+1 along the edges of a (3 dimensional) cube between two opposite vertices.
%C A054880 Urn A initially contains 3 labeled balls while urn B is empty. A ball is randomly selected and switched from one urn to the other. a(n)/3^(2n+1) is the probability that urn A is empty after 2n+1 switches. - _Geoffrey Critzer_, May 23 2013
%H A054880 G. C. Greubel, <a href="/A054880/b054880.txt">Table of n, a(n) for n = 0..1000</a>
%H A054880 G. Benkart and D. Moon, <a href="http://arxiv.org/abs/1409.8154">A Schur-Weyl Duality Approach to Walking on Cubes</a>, arXiv preprint arXiv:1409.8154 [math.RT], 2014 and <a href="http://dx.doi.org/10.1007/s00026-016-0311-3">Ann. Combin. 20 (3) (2016) 397-417</a>
%H A054880 R. J. Mathar, <a href="/A102518/a102518.pdf">Counting Walks on Finite Graphs</a>, Nov 2020, Section 5.
%H A054880 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).
%F A054880 G.f.: (3/4)/(1 - 9*x) - (3/4)/(1 - x).
%F A054880 a(n) = 6*A002452(n).
%F A054880 sin(x)^3 = Sum_{k>=0} (-1)^(k+1)*a(k)*x^(2k+1)/(2k+1)!. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 08 2001
%F A054880 a(n) = A015518(2n+1) - 1 = (A046717(2n+1) - 1)/2. - _M. F. Hasler_, Mar 20 2008
%F A054880 a(n) = 9*a(n-1) + 6 with n > 0, a(0) = 0. - _Vincenzo Librandi_, Aug 07 2010
%F A054880 a(n) = A066443(n) - 1. - _Georg Fischer_, Nov 25 2018
%F A054880 E.g.f.: 3*(exp(9*x) - exp(x))/4. - _G. C. Greubel_, Jul 14 2019
%F A054880 a(n) = 10*a(n-1) - 9*a(n-2) with a(0) = 0 and a(1) = 6. - _Miquel A. Fiol_, Mar 09 2024
%t A054880 Table[(2 n + 1)! Coefficient[Series[Sinh[x]^3, {x, 0, 2 n + 1}],
%t A054880 x^(2 n + 1)], {n, 0, 30}] (* _Geoffrey Critzer_, May 23 2013 *)
%t A054880 LinearRecurrence[{10,-9},{0,6},30] (* _Harvey P. Dale_, Sep 17 2024 *)
%o A054880 (PARI) vector(30, n, n--; 3*(9^n -1)/4) \\ _G. C. Greubel_, Jul 14 2019
%o A054880 (Magma) [3*(9^n -1)/4: n in [0..30]]; // _G. C. Greubel_, Jul 14 2019
%o A054880 (Sage) [3*(9^n -1)/4 for n in (0..30)] # _G. C. Greubel_, Jul 14 2019
%o A054880 (GAP) List([0..30], n-> 3*(9^n -1)/4); # _G. C. Greubel_, Jul 14 2019
%Y A054880 Cf. A002452, A015518, A046717, A066443.
%K A054880 nonn,easy,walk,changed
%O A054880 0,2
%A A054880 Paolo Dominici (pl.dm(AT)libero.it), May 23 2000